The concept of constructibility has been studied in a topological sense: a set is constructible if it belongs to the smallest algebra that contains the open intervals, see for example Chevalley's Theorem: under certain conditions the image under a polynomial map of a constructible set is constructible  [1]}. Equivalently, a set is constructible if and only if it is a finite union of locally closed sets, that is, the intersection of a closed set and an open set (see Lemma REF ). When our initial family  \(\mathcal {U}\)   consists of the open sets, this topological definition matches ours, hence our definition is a generalization of the existing one. In fact, we characterize the constructible sets when  \(\mathcal {U}\)   consists of the open sets, when  \(\mathcal {U}\)   consists of the open intervals and when  \(\mathcal {U}\)   consists of a finite partition. Therefore many of our results apply in the topological case.
